The SAC algorithm is an entropy regularized actor critic algorithm introduced in [1]}.
This work specifically refers to SAC-v2 [2]} as SAC, a slightly improved variant with twin delayed Q networks and automatic entropy tuning.
SAC has a pair of models parameterized by \(\theta \)  and \(\phi \)  that represent the actor \(\pi _\theta \)  and the critic \(Q^\pi _\phi \) .
The critic is a modified version of DQN with entropy regularization that works with continuous action spaces.
The actor is optimized by minimizing the following loss function via the critic:
\( {\begin{array}{c}\mathcal {L}_\pi (Q^\pi _\phi , \pi _\theta ) = - \mathbb {E}_{\begin{array}{c}\mathbf {s}_t\sim \mathcal {D} \\ \mathbf {a}_t\sim \pi _\theta \end{array}} [Q^\pi _\phi (\mathbf {s}_t, \mathbf {a}_t)]\end{array}}\) 
